Highly improved light harvesting and photovoltaic performance in CdTe solar cell with functional designed 1D-photonic crystal via light management engineering

Photonic-based functional designs and integrations for advanced optoelectronic devices are regarded as promising candidates considering the enhancement of efficiency and tunability. With the aim to improve photovoltaic performance by increasing photon harvesting, the study presents the prominent findings of experimental and theoretical comparison of optical and electrical evaluation integrating a functionally designed one-dimension photonic crystal (1D-PC) into CdTe solar cells. Since transparency of the CdS/CdTe heterojunction based solar cell (SC) is reduced by a photonic band gap formed by (MgF2/MoO3)N 1D-PC; namely, re-harvesting is improved by increasing absorbance. The period number at resonance wavelength of 850 nm and photocurrent density (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${J}_{ph}$$\end{document}Jph) have remarkable influence on the investigation. For four periods, the reflectance in the region of photonic band gap is sufficient for photon harvesting and saturation occurs. The photovoltaic performances are comparatively analysed for SCs with and without 1D-PC produced at optimal values. The open-circuit voltage does not change, besides, short-circuit current density and maximum-current density vary between 15.86–17.23 mA cm−2 and, 13.08–15.41 mA cm−2. Having integrated the 1D-PC into the structure, it is concluded that the FF and power conversion efficiency increase from 55.27 to 63.35% with an improvement of 15.91% and, from 8.26 to 10.47% with an improvement of 21.10%.


Results
In the study, the changes in photovoltaic performance result from the integration of the (MgF 2 /MoO 3 ) N 1D-PC system designed inappropriate parameters based on the optical properties of the SC formed in the FTO/SnO 2 / CdS/CdTe/MoO 3 SC were investigated. The investigated FTO/SnO 2 /CdS/CdTe/MoO 3 and FTO/SnO 2 /CdS/CdTe/ MoO 3 /(MgF 2 /MoO 3 ) N SCs are given in Fig. 1a,b, respectively. Fluorine Tin Oxide (FTO) coated on glass substrate was used as the bottom contact in the produced SCs. FTO is electrically conductive and optically highly transparent in the wavelength range for which AM 1.5G is responsible. 100 nm thick SnO 2 was used on FTO due to its wide optical band gap, high optical and electrical properties to prevent recombination of photogenerated carriers. At this thickness, SnO 2 is transparent and at the same time, it provides band arrangement and prevents the leaking of the holes formed by photoproduction to the bottom contact. In this respect, SnO 2 also acts as an electron transport layer (ETL). A 50 nm thick CdS window layer is added to the structure to absorb electromagnetic waves Scientific Reports | (2022) 12:11245 | https://doi.org/10.1038/s41598-022-15078-w www.nature.com/scientificreports/ and transmit photogenerated electrons to the SnO 2 layer. CdS is a promising n-type material from group II-VI and has a wide direct band gap (2.42 eV) 28,29 . In order to increase the photovoltaic performance by creating a large number of electron-hole pairs, CdTe material with an optical band gap of 1.5 eV was chosen as the active layer in the structures produced. CdTe with high material quality can be achieved with the RF sputter technique, especially for submicron thicknesses 30 . In addition to the majority carriers formed as a result of photogeneration, 100 nm thick MoO 3 is used as the BSF layer to localize the minority carriers around the pn junction to collect them more efficiently under the effect of the internal electric field and to reduce recombination. Due to its convenient work function and high p-type doping capability, the formation of ohmic contacts with MoO 3 is both easier and selective transport is provided by preventing photogenerated electrons from reaching the top contact in the structure 13 . In this respect, MoO 3 also acts as a hole transport layer (HTL) in SC. Also, in our previous studies, we have structural and morphological investigations for MoO 3 thin film 31,32 . In order to improve the absorption by reducing the transparency in the FTO/SnO 2 /CdS/CdTe/MoO 3 SC, the photonic band gap in the structure is designed with 1D-PC, which consist of MgF 2 and MoO 3 have different dielectric constants and therefore different refractive indices. The materials excluding the metallization parts were deposited using the RF sputter technique in the SCs examined in the study. The RF sputter technique provides homogeneous and thickness-controlled deposition for CdTe, CdS, and other metal-oxide alloys at the desired stoichiometric ratio 19,30,31,[33][34][35] . In addition, in our previous study, we found that the optical calculations we made with TMM on the devices we produced by deposition with the RF sputter technique showed a nearly perfect agreement with the experiment 19 .
In the examined SCs, the absorber layer is CdTe, which is relatively thicker and has a higher absorption coefficient than the other layers. Therefore, to achieve an increase in photovoltaic performance as a result of only 1D-PC integration without making any modifications to the heterojunction or the SC, first of all, the optical characteristic of the entire SC should be known. Therefore, we started the investigation based on the experimental and calculated transmittance spectra with TMM for the 1D-PC-free SC (FTO/SnO 2 /CdS/CdTe/MoO 3 ). Since the transmittance of the SC will increase in the region where the absorption decreases, we first focused on the longer wavelength region -NIR-, starting from about 700 nm, which is the wavelength region where the transmittance starts and increases. In Fig. 2, the SC's experimental and calculated transmittance spectra, the variation of the absorption coefficient of CdTe and AM 1.5G spectral irradiance depending on the wavelength are given.
The fact that the trends are very close depending on the wavelength in the experimental and theoretical transmittance spectra calculated with TMM in Fig. 2 shows that TMM is a powerful method. CdTe-based SC's were deposited by RF sputter technique and the layers may be deposited with imperfect flatness and slight deviations from the desired thicknesses in terms of nm. This small difference may have occurred because the calculations made with TMM were calculated for the ideal condition of the layers with perfect flatness over the thicknesses in terms of nm. Accordingly, a slight difference is observed in some wavelength regions. The absorption coefficient of the absorber layer CdTe decreases, especially after 800 nm. However, the absorption characteristic is still observed in the NIR region, albeit slightly. The fact that the transparency of the FTO/SnO 2 /CdS/CdTe/ www.nature.com/scientificreports/ MoO 3 SC also increases after 700 means that photons with wavelengths longer than 700 nm pass through the SC without being absorbed. Increasing the absorption by reducing the transparency in this region, i.e., reflecting unabsorbed photons back into the active region and obtaining an efficient harvest, can positively affect the photovoltaic performance of the cell.
In studies on DBR integration into CdS/CdTe-based SCs, only physical interpretation was made on the optical spectra of the DBR layers, and no evaluation was made on the optical properties of the entire SC 9,26 . In addition, the bandwidths were kept quite wide in the related studies and therefore, it was not possible for SCs to work with bifacial illumination. In principle, the refractive indices of the materials that make up the photonic crystal and the contrast of these refractive indices determine the characteristics of the photonic band gap or stop-band to be created with DBR. Increasing the refractive index contrast between materials increases both the reflection intensity and the photonic bandwidth. Therefore, a narrower photonic band gap can be obtained with materials whose refractive indices are closer to each other (less contrast) for a given central wavelength.
We offer a methodologically more effective CdS/CdTe SC design that can be improved in the wavelength region where the absorption is low and can operate under bifacial illumination. For this purpose, we try to reduce the permeability of the with a 1D-PC design with photonic band gap only in the NIR region. Therefore, we calculated the reflectance spectra of the (MgF 2 /MoO 3 ) N 1D-PC system with a central wavelength of B =850 nm at different periods by TMM (Fig. 3). For B =850 nm, the thicknesses of MgF 2 and MoO 3 are 155 and 100 nm, respectively. When Fig. 3 is examined, 1D-PC is designed to act as a mirror in the desired wavelength range according to the mentioned methodology.
The (MoO 3 /MgF 2 ) N 1D-PC system's refractive index contrast is not much, and thus a narrower photonic band gap can be obtained. Increasing the number of periods in the (MgF 2 /MoO 3 ) N 1D-PC system narrows the photonic bandwidth and increases reflection intensity. The rate of increase in the reflection intensity decreases as the number of periods increases. For N = 5 and 6 periods, accumulation starts at 90% reflectance. As expected, the period does not affect the center wavelength. In addition, the short wavelength tail of the photonic band gap formed by the (MgF 2 /MoO 3 ) N 1D-PC system shifts from 657 to 700 nm as the period increases from 1 to 6. Therefore, by integrating the (MgF 2 /MoO 3 ) N 1D-PC system into the FTO/SnO 2 /CdS/CdTe/MoO 3 SC, it is necessary to examine how it affects the increasing SC transparency after 700 nm. The transmittance and absorption spectra were calculated for different periods of the FTO/SnO 2 /CdS/CdTe/MoO 3 /(MgF 2 /MoO 3 ) N SC at B =850 nm are given in Fig. 4a,b, respectively.
As intended, the transmittance spectrum of the FTO/SnO 2 /CdS/CdTe/MoO 3 /(MgF 2 /MoO 3 ) N SC was decreased with the increase of the period number after 700 nm with the (MgF 2 /MoO 3 ) N 1D-PC. Increasing the number of periods up to N = 4 in the SC reduces the transmittance up to 1000 nm to almost zero. At around 700 nm, the intersection of the transparency of the FTO/SnO 2 /CdS/CdTe/MoO 3 SC and the transparency of the (MgF 2 /MoO 3 ) N 1D-PC (Fig. 4a inset) is evident. Therefore, the (MgF 2 /MoO 3 ) N 1D-PC system designed for B =850 nm is a suitable design for CdTe-based SC. In high periods (N > 4), the photonic band gap having sharp lines and decreasing width tends to increase the transmittance around 1000 nm. In order to interpret the effect of this critical change in the optical characteristic of the SC on the photovoltaic performance, it is necessary to examine the absorbance spectrum.
In the FTO/SnO 2 /CdS/CdTe/MoO 3 /(MgF 2 /MoO 3 ) N SC, decreasing the transmittance after 700 nm with the period number directly affects the absorption spectrum, and an increase in absorption was observed after 700 nm. Similar to the trend in the transmittance spectrum, there is no significant increase in absorption in the NIR region with a period number greater than N = 4. In order to examine how this improvement in absorption with www.nature.com/scientificreports/ 1D-PC in CdTe-based SCs affects photovoltaic performance, AM 1.5G spectral irradiance distribution should also be examined. Therefore, for a more effective evaluation, we calculated the absorption characteristic of SC and J ph over S AM1.5G using Eq. (16). Here, when calculating the J ph , it is assumed that each photon creates an electron and a hole in the SC 19 . This situation provides a relative evaluation and allows us to understand whether the flow mechanisms in the SC have improved relatively or not. The variation of J ph in FTO/SnO 2 /CdS/CdTe/ MoO 3 /(MgF 2 /MoO 3 ) N SC according to the number of periods is given in Fig. 5. J ph increases significantly in SC up to N = 4 periods and becomes saturated for higher periods. Increasing the reflection in (MgF 2 /MoO 3 ) N 1D-PC up to N = 4 periods significantly reduces the transmittance of SC, especially by sending photons with wavelengths greater than 700 nm back into the active region. The improvement in absorption by sending photons that were not absorbed in the active region into back with 1D-PC led to re-harvest and increased J ph . Therefore, the integration of (MgF 2 /MoO 3 ) N 1D-PC produced in 4 periods into CdTe-based SC is sufficient for the required re-harvesting of photons. This examination shows that the structural parameters of 1D-PC can be determined experimentally with TMM and an effective methodology without excessive material consumption and fabrication process.
In order to determine how the improvement was brought about by the (MgF 2 /MoO 3 ) N 1D-PC system in J ph affects the photovoltaic performance of the cell and the cell output parameters, we produced the FTO/SnO 2 /CdS/ CdTe/MoO 3 /(MgF 2 /MoO 3 ) 4 SC, which we determined as the optimal N = 4 period. We fabricated SCs with and without 1D-PC at the same parameters and deposition conditions to compare their photovoltaic performances for a quantitative comparison. The J − V and P − V characteristics of FTO/SnO 2 /CdS/CdTe/MoO 3 and FTO/SnO 2 / CdS/CdTe/MoO 3 /(MgF 2 /MoO 3 ) 4 SC are given comparatively in Fig. 6a,b, respectively. Photovoltaic performance outputs obtained and calculated from J − V and P − V characteristics are given in Table 1.
Integration  www.nature.com/scientificreports/ top side provides symmetry for the optical path that light will follow in the SC, since the optical characteristics of these materials are the same, especially for the IR region. Therefore, the transmittance characteristic of the SC does not change under the top and bottom illumination, and the absorption-reflection is in exchange with each other. Modification for the optical trace is done with photonic band gap. This shows that the functional photonic band gap design targeted in the study is methodologically suitable and light management is provided for the SC to work bifacially. As mentioned above, photon harvesting is increased with internal reflection under low illumination, allowing both an improvement in photovoltaic performance and an efficient photon harvest under top illumination.

Discussion
The study was focused on the increment of photon harvesting and improvement of photovoltaic performance with a modifying optical characteristic due to functionally designed 1D-PC integration into CdS/CdTe-based SCs. The absorbance of the SC is enhanced by reducing the transparency with an appropriate photonic band gap which corresponds to the long-wavelength part of the CdTe absorbance band. A photonic band gap was designed with (MgF 2 /MoO 3 ) N 1D-PC, and the optical characteristics of the CdTe-based SC were calculated by TMM. The optimal period number of the PC was determined based on the calculated photocurrent density. In the (MgF 2 / MoO 3 ) N 1D-PC system, which is functionally designed at 850 nm resonance wavelength, the number of periods supports the absorbance by reducing the transparency in the NIR region of the CdTe-based SC. For the period   www.nature.com/scientificreports/ numbers higher than four, accumulation started around 90% reflection and saturation was observed in the J ph . The small-wavelength tail of the photonic band gap formed by 1D-PC system shifted from 657 to 700 nm as the period increases to six. This variation range covered the exact intersection of the transmittance spectrum of the CdTe-based SC and the photonic band gap of the 1D-PC. It has been determined that an optimally four period (MgF 2 /MoO 3 ) 4 1D-PC system is sufficient to increase photon harvesting and improve photovoltaic performance in CdTe-based SCs. CdTe-based SCs with and without 1D-PCs at optimal values were produced under the same deposition conditions and their photovoltaic performances were presented comparatively. It was determined that the (MgF 2 /MoO 3 ) N 1D-PC system did not change the band arrangement in the CdTe-based SC and only affected the optical characteristics. As a result of 1D-PC integration, there was no significant change in V oc , J sc improved from 15.86 to 17.23 mA cm −2 and J m from 13.08 to 15.41 mA cm −2 . These increments in current densities indicated that photons absorbed were reflected into the active region, and, re-harvesting occurred thanks to the photonic band gap designed in NIR. Consequently, FF was improved by 15.91% from 55.27 to 63.35%, and PCE was increased by 21.10% from 8.26 to 10.47%, dependent on the functionally designed 1D-PC integration.
It remains essential to increase photon harvesting and efficiency with light management engineering in 1D-PC and SCs without different material alloying, doping or band alignment. Unlike the studies conducted in the literature for this purpose, designing a functional photonic band gap only in the wavelength region where photon harvesting is weak shows the originality and potential to be a pioneer for future studies of the present study. In addition, the photonic band gap in the study is fine-tuned and functional, as well as not having a conventional wide band gap, allowing light to enter the SC from the top side.
In an overview of the study, it is verified that for the bifacial CdS/CdTe design with 1D-PC, very efficient photon harvesting is provided from the bottom side. Furthermore, an appropriate absorbance characteristic is provided for sufficient photon harvesting from the top side. With TMM, calculations can be made on structures designed by integrating metal layers with different conductivity and dielectric materials. In the most general case, this provides a general framework that allows the calculation of optical characteristics due to the integration of both dielectric, metal, and semiconductor materials with each other. Therefore, we took the most general form as a basis for explaining the calculations and performed the calculations by making the necessary reductions for the structures designed in the study. The plane of a metal layer sandwiched by two dielectrics can be taken as parallel to the z =0 planes. We can examine the propagation of electromagnetic waves on the interface of conductor and dielectric with the configuration and orientation in Fig. 8.
It can be thought that the electromagnetic wave is propagated in the z direction and polarized in the y direction by choosing a special orientation, so that the s and p polarizations can be studied. The magnetic field polarization p can be written in the following form: Here, c is the propagation speed of the light in space, ω is the angular frequency, ε i (i = 1, 2) is the dielectric constant of the i medium, α i and β i (i = 1, 2) are the coefficients. � k i = √ ε i ω/c (i = 1, 2) is the wave vector of the electromagnetic wave. The wavevectors do not change at the material interfaces in the x direction, that is, the x components of the wave vectors at the interface are equal ( k 1x = k 2x ). According to Snell's law, if this situation is applied for the magnetic field and electric field at the interfaces, the following equations are obtained: − → J is the surface current density and n s is the normal unit vector of the surface. According to Ohm's law, the following set of equations can be derived at z=0: where n p = ε 1 k 2z ε 2 k 1z , and ξ p = σ k 2z ε 0 ε 2 ω . With the same methodology, the transition matrix for the s polarization is obtained as follows: where µ 0 is the magnetic permeability of space. The expressions n s and ξ s are equal to k 2z k 1z and σ µ 0 ω k 1z respectively. n p and n s contain the refractive index of the x and y layers. In addition, the complex term includes the absorption coefficient. These values show a direct dependence on the wavelength and the angle of incidence of the electromagnetic wave. Boundary conditions and polarization states can be rewritten in the calculation of optical spectra depending on the angle of incidence of the electromagnetic wave.
All non-diagonal components of the transition matrices show similarity apart from a significant difference, for both s and p polarization. In this way, a common transition matrix for j = (s, p) and η p = 1,η s = −1 can be arranged: The transmission ( t ) and reflection ( r ) coefficients of the electromagnetic wave at the interfaces with the transition matrix and the transmittance ( T ), reflectance (R) and absorbance ( A ) spectra of the structure can be calculated as follows: In the structure given in Fig. 2, when the thickness of the conductive layers is zero, the structure is reduced to the same structure as PC systems, which consist of periodically arranged structures with different refractive indices. In this case, the Bragg wavelength ( B ), which is the center wavelength corresponding to the resonance wavelength of the photonic band gap formed by the PC, must meet the following condition: where n i is the real part of the refractive index of each layer and d i is the layer thickness. For the same optical path in material with different refractive indices, when the n i d i = n j d j condition is met for the photonic crystal quarter-wave stack, the reflection takes its maximum value and coincides with the center of the 1 st order photonic band gap. Therefore, by determining the center of the photonic band gap to be designed, the thickness optimization of each layer in the photonic crystal is done with Eq. (15). As the angle of incidence of the electromagnetic wave increases, the B shifts to short-wavelengths and the bandwidth becomes narrower 25 .
The change in photovoltaic performances as a result of the integration of the 1D-PC, which is designed with the desired photonic band gap and properties, to the SC with CdS/CdTe heterojunction can be examined based on the absorption spectrum of the structure. In FTO/SnO 2 /CdTe/CdS/MoO 3 /(MgF 2 /MoO 3 ) N SC, the absorption characteristic and the wavelength dependent variation of AM 1.5G spectral irradiance ( S AM1.5G ) should be taken into account, significantly to determine how the period number of 1D-PC will change with the J ph that will occur in the cell. For J ph , a calculation has to be made over the entire wavelength range of AM 1.5G spectral irradiance and the following equation is calculated 19,32,39 : Experimental details. FTO/SnO 2 /CdS/CdTe/MoO 3 SC and (MgF 2 /MoO 3 ) N 1D-PC system were deposited using RF sputtering method. Before placing the samples in the sputter system, the FTO-glass substrates were cleaned with alcohol, dried with pure nitrogen gas, and loaded into the Nanovak NVTS500 sputter system. SnO 2 , CdS, CdTe, MoO 3 , MgF 2 targets were loaded on the substrates in the same medium, respectively. All targets used during coating have a diameter of 2", a thickness of 0.250" and a purity of 99.99%. All coatings were carried out in Ar plasma condition at room temperature and 20 mTorr pressure, with a power of 150 W and a rotational speed of 5 rpm. The distance between the target and the substrate holder is 100 mm. In order to provide thickness control and morphological stabilization, we kept the deposition rate as 0.04 Å/s. With a suitable metal choice for CdTe, CdTe will form a Schottky barrier. Because CdTe has a very high electron affinity, a metal with a high work function is required to form an ohmic contact. Therefore, 300 nm thick Au metal contacts were made with the Bestec Thermal Evaporation System by masking in accordance with the design in Fig. 1.
To determine the optical characteristics of the produced SCs, transmittance measurements were taken with the Perkin Elmer Lambda 2S UV-Vis-NIR spectrometer in the 200-1100 nm range. In order to examine the photovoltaic performance of SCs, current density-voltage ( J − V ) characteristics were determined in the dark and AM 1.5G illumination. J − V characteristics Keithley 4200 source meter and Newport Oriel-Sol1A solar simulator are used for AM 1.5G illumination. PCE and filling factor ( FF ) were calculated by determining the short-circuit current density ( J sc ), open-circuit voltage ( V oc ), maximum-current density ( J m ), and maximum voltage ( V m ) from the obtained J − V curves.

Data availability
The datasets generated during and/or analysed during the current study are available from the corresponding author (Ç.Ç.) on reasonable request.